Adaptive Optical Microscopy Using Direct Wavefront Measurements

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1 7 Adaptive Optical Microscopy Using Direct Wavefront Measurements Oscar Azucena University of California at Santa Cruz Xiaodong Tao University of California at Santa Cruz Joel A. Kubby University of California at Santa Cruz 7. Introduction...35 Fluorescent Beads Shack-Hartmann Wavefront Sensor Cross-Correlation Centroiding Reconstruction 7. AO Wide-Field Microscope...3 Fluorescent Microsphere Reference Beacons (Guide Stars) Wavefront Measurements Wavefront Corrections The Isoplanatic Angle and Half-Width Wavefront Corrections and Fluorescent Imaging at Different Wavelengths 7.3 AO Confocal Fluorescence Microscope...38 Optical Setup Results for Fixed Mouse-Brain Tissue 7.4 Using Fluorescent Proteins as Guide Stars Method 7.5 Discussion and Conclusion Introduction The telescope and the microscope have allowed scientists to study the universe and the world we live in (Van Helden 977). Both microscopes and telescopes suffer from optical aberrations created by changes in the index of refraction in the optical path. Dunn and Richards-Kortum (996) have studied the changes in the index of refraction inside biological tissues. Their results indicate that structures with large changes in the index of refraction have large contrast ratios as long as they are near the surface of the biological sample. These changes in the index of refraction degrade the contrast ratio for objects lying much deeper in the tissue. The effect is much worse for samples with a lot of fine structures, since they introduce higher-order aberrations in the images. Schwertner et al. (4) measured the specimeninduced aberrations for a range of typical biological samples (Schwertner 7). Their results indicate that the Zernike-mode representation is a useful tool for describing these aberrations. Their results also indicate that lower-order aberrations are more pronounced than higher-order ones and that spherical aberrations dominate overall. Adaptive optics (AO) is a method used in the telescope for improving astronomical images. Babcock (953) first introduced the idea of improving astronomical seeing by compensating for the atmosphereinduced aberrations. His proposal was to measure the deviations of the light rays from all parts of the mirror and feed that information back so as to locally correct for the deviations. Although the idea was scientifically sound, it had a few minor technical complications, and it was not put into action until years later when the first real-time AO system was used for national-defense applications (Hardy 3 by Taylor & Francis Group, LLC 35

2 36 Applications: Direct Wavefront Sensing 998). AO might have been conceived for the purpose of improving astronomical imaging, but other scientists soon realized the importance of this technology in other areas of research. In particular, vision science was one of those fields where AO has enlightened curious researchers. The first major obstacle in adapting AO to vision science was to find a reasonable reference source for measuring the wavefront. The first Shack-Hartmann wavefront (SHWF) sensor measurements for vision science were realized by Junzhong Liang by imaging a laser spot onto the retina (Liang et al. 994). A few years later, Liang, Williams, and Miller (997) finally constructed the first closed-loop AO system for vision science. The idea of using AO for microscopes is relatively new and a lot of work is still needed. Most AO microscopy systems have so far not directly measured the wavefront because of the complexity of adding a wavefront sensor in an optical system and the lack of a natural point-source reference such as the guide star used in astronomy. Instead, most AO microscopy systems have corrected the wavefront by optimizing a signal received at a photodetector (Booth 7). Debarre et al. (8) have successfully incorporated an AO system into a structured illumination microscope. In his research, Debarre used a wavefront sensorless AO technique in which each mode is corrected independently through the sequential optimization of an image-quality metric. Scientists and engineers have also been investigating ways to implement AO in two-photon microscopes (Marsh, Burns, & Girkin 3; Rueckel, Mack-Bucher, & Denk 6). Rueckel et al. used a coherence gate to selectively pass only the light backscattered near the focus to directly measure the wavefront using an interferometer. Although there are a lot of important researches being done in AO microscopy, many of the AO systems are specific to each microscope, and a universal method for measuring the wavefront (or the results of the correction algorithm) is not currently available. Booth (7) described some of the difficulties associated with the utilization of a SHWF sensor in AO microscopy. Most of these difficulties can be overcome if a suitable fluorescent point-source could be found. Beverage and others found a suitable method for measuring the wavefront of a microscope objective lens by using fluorescent microspheres as reference sources (Beverage, Shack, & Descour ). In his research, Beverage established that bigger beads (larger than diffraction limit) could be used, allowing for more light to measure the wavefront. The size of the beads, d bead, should be smaller than the diffraction limit of the wavefront sensor when imaged through the microscope objective: d bead λ Do =. 44 = d NAob dla DLO ND / d..(7.) where λ is the wavelength at which the beads are emitting, NA ob is the numerical aperture (NA) of the objective, D o is the limiting aperture of the objective, and d LA is the lenslet array pitch. This could also be represented as the diffraction limit of the objective (d DLO ) times the number of subapertures across the limiting pupil. Using this technique, we can measure the aberration introduced by a biological sample by injecting a fluorescent bead into the sample. To reduce the effect of the scattered light, a field stop can be used. The field stop can be placed at the image focal plane just before the wavefront sensor. The system must be designed so that only the wavefront sensor sees the field stop. The field stop will act as a spatial filter, so that the wavefront sensor will not see spatial frequencies above the size of the field stop. To reduce aliasing at the SHWF sensor, the size of the field stop cannot be smaller than d LA as projected onto the image plane (Poyneer, Gavel, & Brase ). 7.. Fluorescent Beads Fluorescent microspheres, with a large variety of colors, are typically used in biology to study..different biological characteristics (Invitrogen Corporation ; Rothwell & Sullivan ; Guldband et al. ; DeMarais, Oldis, & Quatrro, 5; Rowning et al. 997; Kalpin, Daily, & Sullivan 994). The microspheres are made of polymers and are impregnated with different fluorescent dyes. The microspheres can be 3 by Taylor & Francis Group, LLC

3 Adaptive Optical Microscopy Using Direct Wavefront Measurements 37 engineered with coatings to preserve them in different conditions and can be made to target different biological tissues, organelles, cell walls, or other biological structures (Invitrogen Corporation, ). They can be introduced into the sample by different mechanisms such as negative pressure injection, pressure injection, matrotrophycally, diffusion, and others (Guldband et al. ; DeMarais, Oldis, & Quatrro 5; Rowning et al. 997). In particular, fluorescent microspheres have been injected previously in Drosophila embryos (Kalpin, Daily, & Sullivan 994). Sufficiently small fluorescent microspheres, as described earlier, are diffraction-limited when imaged by the SHWF sensor, enabling their use as point-source reference beacons for the operation of the SHWF sensor. Azucena et al. () show that..multiple beads can also be used to directly measure the wavefront. The wavefront measurements from multiple beads and a single bead differ only in the higher-order aberrations (e.g., above the seventh radial order Zernike). 7.. Shack-Hartmann Wavefront Sensor A SHWF sensor samples the wavefront at different points of the pupil by using a lenslet array to measure the mean slope across each subaperture as shown in Figure 7.. On the one hand, Figure 7.a shows a flat wavefront impinging onto the SHWF sensor; as can be seen, there is a slope of zero measured at each of the Hartmann spots. Figure 7.b, on the other hand, shows a distorted wavefront impinging onto the SHWF sensor. The spot displacement at each subaperture is directly proportional to the product of the mean slope at the subaperture and the focal length of the lenslet. The wavefront can be reconstructed using Equations 7. and 7.3 (Liang et al., 994): w ( x, y ) x w ( x, y ) y = x..(7.) fla i i i = y..(7.3) fla i i i Flat wavefront CCD Aberrated wavefront CCD d s d s Lenslet array (a) (b) FIGuRE 7. A Shack-Hartmann wavefront sensor measures the mean slope at each subaperture; this..information is used to reconstruct the wavefront over the whole aperture. (a) Flat wavefront; (b) distorted wavefront. 3 by Taylor & Francis Group, LLC

4 38 Applications: Direct Wavefront Sensing where ƒ LA is the focal length of the lenslet array, Δx and Δy are the slope measurements at the.subaperture i in the x and y directions, respectively, and w(x i,y i ) is the wavefront at the point x i and y i Cross-Correlation Centroiding Many astronomy AO systems use a quad-cell detector in the SHWF sensor to determine the mean slope at each subaperture (Hardy 998). Although the quad cell may be very easy to implement, it images the sub.aperture into four pixels, so it can be used to detect only approximately half a wavelength of tilt at each subaperture. To overcome the limitations of the quad cell, more pixels per subaperture are needed to better sample the Hartmann spots. Introducing more pixels does have the negative effect of increasing the effects of noise, which current detectors have not managed to overcome. On the other hand, there are many algorithms that help overcome the effects of noise (Thomas et al. 6; Adkin, Azucena, & Nelson 6; Poyneer 3). The cross-correlation algorithm requires a reference Hartmann spot with which all the Hartmann spots will be compared to. The reference image shown in Figure 7. is first analyzed to acquire the image of a Hartmann spot. Figure 7.3 shows the average Hartmann spot of the reference image in Figure 7.. In a real time AO system, the reference spot should not be oversampled too much, since a lot of resources are required to analyze the data. Thomas et al. (6) suggested that the Hartmann spot Figure 7. SHWF sensor image with a microsphere as the reference source. Left: The raw WFS data; Right: The same image with the subapertures separated. Reference image y (pixels) x (pixels) Figure 7.3 Average Hartmann spot, obtained by finding the maximum of each subaperture in Figure 7. and adding all the images around their corresponding maxima. 3 by Taylor & Francis Group, LLC

5 Adaptive Optical Microscopy Using Direct Wavefront Measurements 39 should be imaged into an area of pixels to acquire the most information without losing precision in centroiding. One of the advantages of using the cross-correlation algorithm is that the computation can be done in the Fourier domain, taking advantage of the Fast Fourier Transform (FFT) algorithm available to improve the speed of the AO system. Although the reference function can be modeled as a Gaussian spot, it can be shown that using a real-time Hartmann-spot measurement from the SHWF sensor images can improve the accuracy of the centroiding algorithm (Thomas et al. 6). This is mainly due to the amount of information afforded by the real-time spot measurement compared to that of a Gaussian image. The final step needed to measure the amount of slope at each subaperture using the cross-correlation algorithm is to find the maximum for each subaperture (Thomas et al. 6) Reconstruction There are various ways of estimating a wavefront from the Hartmann slopes (Hardy 998; Gavel 3). Two essential pieces of information are needed for this: () the phase difference (slope measurements times subaperture size) from each subaperture and () the geometrical layout of the subapertures. The wavefront can then be calculated by relating the slope measurement to the phases at the edge of the subaperture in the correct geometrical order. A method for directly obtaining the deformable mirror (DM) commands from wavefront sensor measurements is described by Tyson (998). First a mask with the subapertures must be created; this will generate the geometric layout of the subapertures in the aperture. The next step is to measure and record the response of all the subaperture slope changes while actuating each actuator. The results obtained are set of linear equations that show the response of the wavefront sensor for each actuator command known as the poke matrix (also known as the actuator influence matrix). The DM commands can then be obtained by solving the equation s = Av (7.4) where s is an n-size vector obtained from the SHWF sensor slope measurements, v is an m-size vector with the DM actuator commands, and A is an n m sized poke matrix. In the linear approximation, Equation 7.4 can be pseudo-inverted to obtain an estimate of the DM command matrix. Note that the DMs are nonlinear devices, but the matrix given in Equation 7.4 performs well in a closed-loop system, as only very small voltage changes occur, thus reducing the nonlinear effects. There are various methods for inverting the matrix A, including singular value decomposition (SVD). The advantage of using SVD is that the mode space can be directly calculated. The noisier modes, and all the null space modes by default, can then be removed by setting a threshold on the singular value space (Gavel 3). Figure 7.4a shows a poke matrix obtained by using the method described here. The process begins by poking an actuator to a predetermined voltage (V); each of the subapertures slope changes is then recorded. This process is repeated times for each actuator, and the recorded data are then averaged to reduce the effect of noise. The slope changes are determined using the cross-correlation centroiding algorithm. Further conditioning of the poke matrix is performed by thresholding the data to % of the maximum slope changes measured for all actuators. For each actuator poke, there will be an area in the SHWF sensor that will show stronger slope changes (i.e., an influence function). In AO, a 5 % influence function between actuators is usually considered good as this allows for high spatial deformations to be well reproduced by the DM. The thresholding step mentioned earlier essentially windows the slope measurements to an area near the center of the actuator poke with a % slope influence matrix. Considering a larger area can introduce higher spatial frequencies that are dominated by noise, thus introducing noisier modes into our singular-value space. Figure 7.4b shows the singular-value pseudo inverse of the poke matrix shown in Figure 7.4a. The pseudo inverse has the singular-value space shown in Figure 7.4c, which has been regularized to remove the singular-value modes that are lower than 5% of the maximum mode as described by Gavel (3). By multiplying the poke matrix in Figure 7.4a and its pseudo inverse in Figure 7.4b, the actuator space 3 by Taylor & Francis Group, LLC

6 3 Applications: Direct Wavefront Sensing (a) Poke matrix.987 (c) Singular values (b) Pseudo inverse.393 (d) Actuator space.78 Figure 7.4 (See color insert.) (a) Poke matrix obtained by the method described in the main text. (b) SVD inverse of the matrix in (a). (c) Singular-value modes with modes lower than 5% of maximum mode have been removed. (d) Actuator space obtained by multiplying (a) and (b). can be obtained as shown in Figure 7.4d. By analyzing the diagonal of the product matrix, each actuator response can be determined. In particular, the actuators that have little or no effect on the system can be detected, and the actuators that are too far from the aperture can be removed as they have no registration on the poke matrix. 7. AO Wide-Field Microscope Figure 7.5 shows the design of an AO wide-field microscope. An AO system was added to the back port of an Olympus IX7 inverted microscope (Olympus Microscope, Center Valley, PA). This allowed use of the side image port for point spread function (PSF) measurements, which were compared with the PSF viewed after the AO system to ensure that the AO system did not add aberrations. Using a camera with very small pixels (flea with 4.65 μm pixels, Point Grey, NY), we were able to verify a very close match between the PSF before and after the AO system. The AO system was designed around an Olympus 6X oil-immersion objective (Ob) with an NA of.4 and a working distance of.5 mm. Lenses L and L have 8 and 85 mm focal lengths, respectively, and are used to image the back pupil of the 6 objective onto the DM (Boston Micromachines, Boston, MA). The DM has 4 actuators on a square array with a pitch of 4 μm, a stroke of 3.5 μm, and an aperture of 4.4 mm. Note that.5 μm of stroke was lost to AO path compensation and flattening of the DM. L3 and L4 are 75- and 5-mm focal length lenses, respectively, and are used to reimage the back pupil of the objective onto the SHWF sensor. The system has two illumination and imaging arms: the first is a science arm in which we used a set of..filters F and F (Semrock, Rochester, NY) to redirect a beam from an argon 488 nm laser (blue laser) to the objective for excitation of a green fluorescent sample. The light emitted from the green fluorescent sample is imaged by the green science camera (green SC). Filter F3 (Semrock) is used to redirect the HeNe 63.8 nm laser (red 3 by Taylor & Francis Group, LLC

7 Adaptive Optical Microscopy Using Direct Wavefront Measurements 3 Sample Blue laser Green SC Red laser Crimson SC Ob IX7 L F L D L3 L4 F F3 BS SHWS DM FIGuRE 7.5 AO wide-field microscope setup. DM, SHWS, 488 nm laser (blue laser), green flourescent science camera (green SC), HeNe 63.8 nm laser (red laser), crimson flourescent science camera (Crimson SC). L, L, L3, and L4 are 8, 85, 75, and 5 mm focal length lenses, respectively. Fold mirror D helps to bring the optical path into alignment for the SHWS. Green SC Crimson SC SHWS DM FIGuRE 7.6 Adaptive optics wide-field microscope set up with Olympus IX7 inverted microscope and Boston Micromachines DM. laser) through a confocal illuminator (not shown) onto the optical path for excitation of the crimson reference beads (Azucena et al., a). This confocal illuminator allows us to illuminate a single crimson reference bead to create a single diffraction-limited spot. The beam splitter (BS) lets 9% of the emitted light coming from the crimson reference beads go to the SHWF sensor for wavefront measurement and % for.imaging in the Crimson Science Camera (Crimson SC). The SHWF sensor is composed of a element lenslet array each with a focal length of 4 mm and a diameter d LA = 38 μm (AOA Inc., Cambridge, MA), and a cooled CCD camera (Roper Scientific, Acton, NJ). Figure 7.6 shows the setup on the optical table, highlighting a few of the components like the DM, science cameras, and SHWF sensor. 7.. Fluorescent Microsphere Reference Beacons (Guide Stars) We have developed a microsphere injection process, which works very well for introducing reference beacons, or guide stars, into live embryos. This process does not harm the embryos as they have the ability to heal the wound around the injection site. Using a : concentration microsphere solution assures that there will be a microsphere within μm of the center of the injection discharge. The microspheres spread in a random manner around the discharge site and can usually be found to spread 3 by Taylor & Francis Group, LLC

8 3 Applications: Direct Wavefront Sensing Microspheres Injection site Figure 7.7 Combination of a differential interference contrast image and a confocal image of injected microspheres in fruit-fly embryo 4 μm below the surface of the embryo. The white bar in the figure is μm long. throughout the embryo. Figure 7.7, a combination of a differential interference contrast (DIC) image and a confocal image, both taken with a Leitz inverted photoscope equipped with laser confocal imaging system (Leica Microsystems, Bannockburn, IL), illustrates that relative to the injection site and the embryo walls, the microspheres have spread randomly inside the embryo. A higher microsphere concentration could also be used as the optical setup shown in Figure 7.5 allows for the laser to illuminate one bead at the time. A bead concentration as high as : has been used, and the results show many more beads available in the field of view (FOV). 7.. Wavefront Measurements A reference Hartmann sensor image was obtained to cancel the aberrations introduced by the optical setup and coverslip. The reference image was taken by imaging a single fluorescent bead onto the Hartmann sensor. The bead was dried onto a glass slide and imaged with the coverslip and mounting media. The image was processed to obtain the location of the Hartmann spots using the cross-. correlation centroiding algorithm described earlier. For each wavefront measurement, a new Hartmann sensor image was acquired with the sample prepared as described in the Section 7... The new measurement was then processed to determine the displacement of the Hartmann spots (slope measurements) relative to the reference image described earlier. The slope measurements were finally processed to obtain the wavefront by using an FFT reconstruction algorithm (Poyneer, Gavel, & Brase ). For each measurement, the peak-to-valley (PV) and the root-mean-square (RMS) wavefront errors were collected. The wavefront function was also expanded into the Zernike s circle polynomials to determine the relative strength of the different modes (Porter et al. 6; Poyneer 3). The Zernike polynomials are normalized and indexed as described by Porter et al. (6). The wavefront measurements were also used to analyze the PSF by taking the Fourier transform of the complex pupil function: PSF( x, y) = π FT P( x', y') exp i w( x', y') λ FT { P( x', y') } ξ=, η= x y ξ=, η= λ f λ f..(7.5) where P is one inside the pupil and zero everywhere else, x and y are the coordinates at the pupil plane, ξ and η are the spatial frequencies in the transform domain, x and y are the coordinates at the 3 by Taylor & Francis Group, LLC

9 Adaptive Optical Microscopy Using Direct Wavefront Measurements 33 image plane, w is the wavefront measurement, and λ is the wavelength at which the measurement was taken. A measurement of the wavefront from a μm crimson fluorescent microsphere embedded 45 μm below the surface of a Drosophila embryo using a dry (.4 NA) objective lens is shown in Figure 7.8. The distance between points is equal to the subaperture diameter, d LA., for a total of 6 apertures on the circular pupil. As can be seen from Figure 7.8, the PV wavefront error is ~.56 μm and the RMS wavefront error for this measurement is.9 μm. Figure 7.9 shows the Zernike coefficients for the wavefront shown in Figure 7.8. As can Wavefront with no Tip, Tilt, and Focus Y (Apertures) X (Apertures) FIGuRE 7.8 A wavefront measurement from a μm fluorescent microsphere embedded 45 μm below the surface of a Drosophila embryo using a (.4 NA) objective lens with tip, tilt, and focus subtracted. The x and y axes are scaled to the subaperture diameter. The grayscale is labeled in micrometers..3 Zernike coefficient value Astigmatism Zernike coefficient value [microns].... Astigmatism Zernike coefficient index FIGuRE 7.9 Zernike coefficient values for the wavefront shown in Figure 7.8. Astigmatism is labeled. 3 by Taylor & Francis Group, LLC

10 34 Applications: Direct Wavefront Sensing PSF (a) Normalized PSF (b) (c) 4 3 y μm x μm 5 Ideal PSF Calculated PSF Corrected(4) PSF Normalized PSF.5 Normalized PSF.5 Normalized PSF.5 4 x μm (d) 4 4 x μm (e) 4 4 x μm (f) 4 Figure 7. PSF analysis. (a) Calculated using a flat wavefront. (b) Calculated using the wavefront shown in Figure 7.8. (c) Calculated by removing the first 4 Zernike modes of Figure 7.8. (d) Cross-sectional view of (a). (e) Cross-sectional view of (b). (f) Cross-sectional view of (c). be seen from Figures 7.8 and 7.9, astigmatism and spherical aberrations dominate the wavefront error. This is mainly due to the index mismatches in the optical path and the curved body of the embryo, which mostly introduced the lower-order aberrations. Note that the optical aberrations due to the coverslip and air-glass interface, including tip, tilt, and focus, have been removed by the reference image. A reassuring sign shown in Figure 7.9 is that the amplitude of the higher-order aberrations are decreasing, and therefore, by correcting a finite number of Zernike modes, the imaging qualities of the optical system can be expected to improve. Note that the spatial resolution for the wavefront measurement setup for the objective with a limiting aperture D = 5.9 mm is the Zernike mode so that the decreasing amplitudes shown in Figure 7.9 are not an artifact of the sensor. The spatial resolution of the SHWF sensor is directly proportional to the number of degrees of freedom (i.e., the number of subapertures inside the pupil) (Porter et al. 6). Figure 7.a shows the PSF for an optical system with no aberrations. Figure 7.b displays the PSF calculated by using Equation 7.5 and the wavefront shown in Figure 7.8. The Strehl ratio is defined as the ratio of the peak intensity of the PSF relative to the peak intensity of the diffraction-limited PSF (Porter et al. 6). Figure 7.e shows that the Strehl ratio is approximately.37. The effect of removing the first 4 Zernike modes can be seen in Figure 7.c and f. Using this simulation, we can estimate that correcting the first 4 Zernike modes will improve the Strehl ratio to.7. Table 7. shows the statistical data gathered from the measurements taken. Each measurement comes from different fluorescent microspheres ranging in depth from 4 to μm below the surface of the 3 by Taylor & Francis Group, LLC

11 Adaptive Optical Microscopy Using Direct Wavefront Measurements 35 Table 7. Statistical Data for Dry (.4 NA) and Dry 4 (.75 NA) Objectives No. PV (μm) RMS (μm) S S(4) Mean Mean PV, Peak-to-valley; RMS, root-mean-square; S, Strelh; S(4), Strehl after correcting first 4 Zernike modes embryo. The measurement error for the SHWF sensor was measured to be less than 5% of the wavelength at 647 nm. This was measured by repeating a single measurement times and measuring the RMS error for that one data point. Measurements 9 were taken with a objective; measurements 4 6 were taken with a dry 4 objective. The measurements show a maximum PV wavefront error of.88 and.37 μm for the and 4 lenses, respectively. The maximum RMS wavefront error was.3 and.9 μm for the and 4 objective lenses, respectively. This demonstrates only some of the typical aberrations that can be encountered for the Drosophila melanogaster sample. For a similar study on some of the early phases of this work, please see Azucena et al. (). The higher PV and RMS measurement in the 4 objective are mainly due to the spherical aberrations introduced by the higher NA lens. Table 7. also shows the Strehl ratio (column four) obtained by finding the global maximum of the PSF image for each measurement using a search algorithm in MATLAB. By removing different Zernike modes, we can also approximate the effect of removing different amounts of wavefront error. Column 5 in Table 7. demonstrates the effect of removing the first 4 Zernike modes from each measurement. The data show that correcting a small number of modes improves the imaging capabilities of the system. Figure 7. shows the statistical data for each Zernike mode for the measurements shown in Table 7.. The data show a gradual decrease in value with increasing Zernike mode. From this we can verify that loworder aberrations are the main source of wavefront error and that the aberration values are higher in the 4 objective. The gradual decrease in the strength of each Zernike value for higher Zernike modes shows that there is little wavefront aberration introduced for modes higher than 5, which is well within the range of our sensing capabilities. Note that the spatial resolution for the wavefront measurement setup for the 4 objective with a limiting aperture D = 3 mm is the Zernike mode. This helps to verify the simulation results obtained in Figure 7. that correcting only a few low-order Zernike modes helps to improve the Strehl ratio by at least a factor of two. This point will also be shown again in our correction of the wavefront that follows Wavefront Corrections Validation of the wavefront measurements can be obtained by correcting the wavefront and thus closing the loop in our system. Figure 7. shows the results of the correction steps, where each correction step 3 by Taylor & Francis Group, LLC

12 36 Applications: Direct Wavefront Sensing Zernike value (μm).4. Absolute mean Zernike value (μm).5 Absolute mean 4 Zernike mode Zernike mode (a) (c) Zernike value (μm). RMS RMS 4 Zernike value (μm).4. Zernike mode Zernike mode (b) (d) Figure 7. Zernike statistical data for the measurements in Table 7.. (a) and (b) The mean of the absolute value and the RMS values for each Zernike mode for the objective (.4 NA), respectively. (c) and (d) The mean of the absolute value and the RMS values for each Zernike mode for the 4 objective (.75 NA), respectively. was ms apart. Each correction was done using the light coming from a single bead to directly measure the wavefront. The measurement was then fed back to the DM by using a proportional gain of.4, which was the highest possible gain for this sample before the onset of oscillations (Lyapunov stability criteria) (Slotine & Li 99). The AO loop gain can be described by the feedback equation W( s) E( s) = W( s) D( s) = W( s) H( s) =..(7.6) + KD( s) G( s) where E(s) is the wavefront error measured by the wavefront sensor, W(s) is the Fourier transform of the input wavefront coming from the sample, H(s) is the transfer function of the AO system, G(s) is the transfer function of wavefront sensor, D(s) is the transfer function of the DM, and K is the gain on the feedback loop (.4). The goal of the AO system is to reduce the difference between the applied phase on the mirror and the incoming wavefront, the error E(s), thus flattening the wavefront (Hardy 998; Poyneer, Gavel, & Brase ). In AO, DM correction usually requires a gradual change in shape to account for the nonlinearity of the wavefront sensor and the DM. This comes about mainly due to the nonlinear effects of the DM and secondly (usually much smaller) due to the nonlinear effects of the SHWF sensor. The nonlinear effects of the DM come from the nonlinear dependence of the electrostatic actuation force on the applied voltage and plate separation for a parallel plate actuator and the nonlinear restoring force from stretching of both the mechanical spring layer and the mirror surface. Figure 7.a shows the original PSF of the microsphere before correction taken with the science camera. Figure 7.b shows the result of correcting for 4% of the measured wavefront error in Figure 7.a. These steps were repeated until there was no additional significant reduction in wavefront error (i.e., <7 nm). Figure 7.e demonstrates the results of correcting the wavefront after four steps in the AO loop. Each image has been normalized to its own maximum to clearly show the details of the PSF. The bar in Figure 7.c is approximately equal to the diffraction limit of the 4 objective,.45 μm. The..improvement in Strehl was approximately. The relative Strehl ratio S was obtained by measuring the peak intensity in Figure 7.a divided by the peak intensity in Figure 7.e using the same integration time Δt for each, as shown in Equation 7.7: 3 by Taylor & Francis Group, LLC

13 37 Adaptive Optical Microscopy Using Direct Wavefront Measurements (a) (b) (c) (d) (e) Figure 7. AO microscope loop correction steps. (a) An uncorrected image of the fluorescent microsphere. (b) (e) Result of closing the loop by using a loop gain factor of.4. The length of the bar in (c) is equal to the diffraction limit of the 4 (.75 NA) objective lens,.45 μm. The bead was located μm beneath the surface of the embryo. DM Shape Wavefront Y (Apertures) Y (Apertures) X (Apertures) (a) X (Apertures) (b) 4 Figure 7.3 (a) Initial wavefront measurement. (b) Closed-loop DM wavefront. The legend is scaled in percent wavelength at 65 nm. Srelative = I peak,e I peak,a (7.7) Figure 7.3 shows the initial wavefront measurement (wavefront before correction loops started) and the final shape of the DM for the adaptive loop corrections seen in Figure 7.. The DM shape was obtained by summing the shape commands that were sent to the DM for each loop step. The small steps in voltage reduce the nonlinear effects from the DM since only small changes in the mirror surface are produced for each time step. There was a 3 nm RMS error difference between the final DM shape and the original wavefront measurement. The final error between these measurements can be partly attributed to the wavefront reconstructor. The effect comes from the lack of measurements outside the edge of the aperture (Poyneer, Gavel, & Brase ). The DM wavefront is inverted to help comparison of the wavefront error and the mirror shape The Isoplanatic Angle and Half-Width The isoplanatic angle is a relative measure of the FOV over which the AO system can operate and is defined as (Hardy 998) σ θ = ( ϕ( X, ) ϕ( X, θ )) = rad 3 by Taylor & Francis Group, LLC (7.8)

14 38 Applications: Direct Wavefront Sensing Table 7. Isoplanatic Angle Measurements for the 4 Magnification,.75 NA Objective Lens Mean 9 ± ± ±.39.4 ± ±.3 where φ is the wavefront in radians, X is a vector representing the two-dimensional (D) coordinates, θ is the isoplanatic angle, and σ θ is the mean-square error between the measured and observed wavefront. We can determine the isoplanatic half-width by multiplying the isoplanatic angle by the focal length of the objective. To determine the isoplanatic angle, we took wavefront measurements from two microspheres separated by a distance d. A microsphere was excited by shining a laser on it. Each microsphere was excited individually. Each wavefront sensor measurement was collected over a period of 5 ms, much longer than the typical AO loop bandwidth. This ensures that there is little noise on the data. The standard deviation for each individual wavefront was measured to better than % of the wavelength at 647 nm. Table 7. shows three different measurements taken with a 4 (.75 NA) objective lens. The first measurement shows that the wavefront error for the bead located at the center of the FOV RMS() is.6 radians, the wavefront error for the bead located 4 μm from the center RMS() is.9 radians, and the wavefront difference between the two measurements RMS( ) is.73 radians. Taking the average of three measurements shows that the isoplanatic half width is 9 ± 5.6 μm. These results show that a reference microsphere together with an AO system can help improve the quality of the images taken, not just at the location of the microsphere but also within a circle μm in radius Wavefront Corrections and Fluorescent Imaging at Different Wavelengths We have taken wavefront measurements at one wavelength (red) that have been used to make corrections to fluorescently labeled beads at a different wavelength (green). Green beads were used to emulate biological structures that are labeled with green fluorescent protein (GFP) using well-known structures that have a size ( μm) that is near the diffraction limit of the optical system. The images in Figure 7.4 are of green fluorescent beads that were excited using the 488 nm laser and imaged with the green science camera (Azucena et al. ). In Figure 7.4a, the AO system is off, and the mirror was put on a flat position that had been calibrated using an interferometer. The flat position is kept on regardless of correction on or off to reduce systematic aberrations. We can see some details about structures μm below the surface of the embryo, but we are not able to resolve the individual beads that make up the clumps of material shown in the image. In Figure 7.4b, the AO system had been turned on, and we can clearly resolve the individual μm fluorescent beads. Figure 7.4c and d show cross-sectional profiles along the gray lines in Figure 7.4a and b, respectively. These figures show that with the AO system on, we can clearly resolve the individual beads and thus are able to obtain higher resolution structural information. Even though the wavefront aberrations were measured using the crimson beads, the corrections applied to the mirror still improve the image of the green fluorescent beads, which are more than nm apart in wavelength. 7.3 AO Confocal Fluorescence Microscope The principle of the confocal microscope is shown in Figure 7.5. A patent on this invention was filed in 957 by Marvin Minsky and was issued in 96 (Minsky 96). The focal plane of a coherent light from a laser source is conjugate with the pinhole located in front of the detector. The light is reflected by a dichromatic mirror and focused on the sample through an objective lens. The emission light from the 3 by Taylor & Francis Group, LLC

15 Adaptive Optical Microscopy Using Direct Wavefront Measurements 39 (a) (b) (c) Intensity (au) 5 5 (d) 5 Intensity (au) Distance along profile (. μm) Distance along profile (. μm) FIGuRE 7.4 (See color insert.) Real-time AO correction of μm green fluorescent microspheres μm beneath the surface of a fruit-fly embryo, using a μm crimson fluorescent microsphere guide-star located at the center of the image. The size of the scale bar in the figures is μm. Detector pinhole Excitation filter Laser Photomultiplier detector Emission filter Light source pinhole Dichromatic mirror Objective Focal plane FIGuRE 7.5 Diagram of a confocal microscope. 3 by Taylor & Francis Group, LLC

16 33 Applications: Direct Wavefront Sensing sample passes through the objective lens and dichromatic mirror and focuses on the detector pinhole. Because the focal plane and the detector pinhole all share the same conjugate plane, only the light from the focal plane can pass through the detector pinhole. This minimizes the background fluorescence and improves the contrast of the final image. Compared to the light from the focal plane, the effect of the background light on the final image is negligible. The excitation filter is used for the selection of the excitation wavelength of the light source, which is especially important when a multichannel excitation laser source is used. The dichromatic mirror is used to separate the excitation and emission light paths. The emission filter selects the emission wavelength of the light more narrowly and removes any traces of excitation light. To obtain a D image, a confocal microscope is often equipped with a D scanner and a Z scanning stage, which can provide lateral sections (x-y plane) and vertical sections (x-z and y-z planes). With a fast resonant scanner or a spinning disk, the confocal microscope can provide real-time imaging Optical Setup Figure 7.6 shows the layout of the AO confocal fluorescence microscope (AOCFM). The whole system was designed and optimized using the optical design software (CODE V). A 6 water-immersion objective with a NA of. was used (Olympus Microscope, Center Valley, PA) for imaging of both fixed and living cells. The optical system includes three telescope relay subsystems. Lenses L and L image the exit pupil of the objective onto the Y scanner. Lenses L3 and L4 relay the X scanner conjugate onto the Y scanner. This design minimizes the movement of the scanning beam at the exit pupil of the objective and the emission light at the DM, which is important for accurate wavefront measurement and correction. The lenses L and L3 also serve as scanning lenses. The current design is optimized for an optical scanning angle of 4.4, which provides a FOV of 8 μm on the sample with the 6 objective. By changing the control signal to the scanners, the FOV can be easily adjusted. Lens L5 and L6 image the pupil of the X scanner onto the DM. Lenses L7 and L8 image the pupil of the DM onto the wavefront sensor. The DM (Boston Micromachines) has 4 actuators and 3.5 μm of stroke. The diameter of the effective aperture on the DM used in this design is 4 mm, which is slightly smaller than the 4.4 mm of aperture of the mirror, to decrease edge effect. The exit pupil of the objective is 7. mm. To match the aperture of the DM with the objective, the telescope formed by L and L demagnifies the pupil from 7. to 4 mm. A HeNe laser emits light at 633 nm for excitation of the crimson fluorescent reference beacon. A solidstate laser emits light at 55 nm that excites yellow fluorescent protein (YFP) bred into the sample. F and F4 are excitation filters. Light emitted from the reference beacon is passed through filter F to the Wavefront sensor Science camera L9 F Helium neon laser (633 nm) DB X Scanner F L8 F3 DB3 L7 Pinhole L5 L4 PMT DB Pinhole L F4 L6 Pinhole L3 Solid-state laser (55 nm) DM Y Scanner L F: Filter DB: Dichroic beamsplitters Tube lens Objectives L FIGuRE 7.6 System layout of the adaptive optics confocal microscope. 3 by Taylor & Francis Group, LLC

17 Adaptive Optical Microscopy Using Direct Wavefront Measurements 33 wavefront sensor. The SHWF sensor is composed of a element lenslet array with a lenslet diameter of 4 μm and focal length of 4 mm (AOA Inc., Cambridge, MA) and an electron multiplying CCD (EMCCD) camera (Cascade II, Photometrics). The dichroic BS DB separates the light from the crimson reference beacon and the YFP-labeled sample. The dichroic BSs DB and DB3 are used to separate the excitation light and its associated back reflection. The fluorescent light emitted by the YFP is filtered by F3 and detected by the photomultiplier tube (PMT). The wavefront aberration is corrected by the DM. Two laser channels are included in the system: a solid-state laser (λ = 55 nm) and a helium-neon laser (λ = 633 nm) used for confocal fluorescence imaging and wavefront sensing, respectively. The two channels share the same light path through the DM, relay lenses, scanner, and scanning lens and feed into an Olympus IX7 inverted microscope (Olympus Microscope, Center Valley, PA) through its side optical port. The focused beam is scanned on the sample in a raster pattern with a resonant scanner (SC-3, 6 khz, 5, Electro-Optics Products Corp.) and a vertical scanner (GVS, Thorlabs). The control signals for the scanners are generated by a data-acquisition board (PCIe-6363, National Instruments Corporation). The emission light from both the crimson microsphere guide-star and the YFP-labeled sample are collected by an objective lens (Olympus 6, NA. water immersion) and separated by a dichroic mirror (DB). The light from the sample was focused onto a pinhole by an achromatic lens L. A GaAs PMT (H4-5, Hamamatsu) was used as a photon detector. The signal from the PMT is then fed to a frame-grabber board (Helios ea/xa, Matrox Imaging). With the vertical and horizontal synchronized signal from the DAQ, the frame-grabber board generates a raw image of 5 5 pixels at 3 frames/second for live imaging. When the signal levels are low, more frames can be averaged to increase the signal-to-noise ratio (SNR). We have also used two galvo scanners (65H, Cambridge Technologies) at lower frame rates (3 Hz) to increase the SNR. The experimental system was setup on an optical table with vibration isolation as shown in Figure 7.7. The beam from the scanning system was fed into the Olympus IX7 inverted microscope by a periscope Results for Fixed Mouse-Brain Tissue To investigate the feasibility of the proposed system, a fixed brain slice from a YFP-H line transgenic mouse was prepared. YFP is labeled on the cell body and protrusions of the neurons. One micron Science camera HeNe laser PMT Olympus X6 Frame Solid state laser DM SH Wavefront sensor X Scanner Y Scanner FIGuRE 7.7 Experimental setup of an adaptive optics confocal microscope. The system was setup on an optical table with vibration isolation. The optical path for the crimson reference beacon (guide star) is shown as a white solid line. A HeNe laser is used for excitation of the guide star and its emission wavefront is measured with a Shack- Hartman wavefront sensor. The optical path from the microscope to the photomultiplier tube (PMT) for detecting the sample fluorescent emission (YFP) is shown as a dashed line. The excitation path for the sample (55 nm solidstate laser) is shown as a grey solid line. 3 by Taylor & Francis Group, LLC

18 33 Applications: Direct Wavefront Sensing Microspheres (a) (b) FIGuRE 7.8 Wide-field microscopy images of mouse-brain tissue (thickness = μm) with (a) objective and (b) 6 water immersion objective. The focal plane is at the bottom of the tissue. The microsphere is deposited on the glass slide. (a) (b) FIGuRE 7.9 Confocal imaging of mouse-brain tissue without AO. The thickness of tissue is μm. (a) The image on the top surface of the sample. (b) The confocal image at the bottom surface of the sample. diameter crimson fluorescent microspheres (Invitrogen, Carlsbad, CA) were deposited onto a glass slide and below a cover plate for use as laser guide-stars. Sample brain coronal sections of different thicknesses (5, 5, and μm) were cut with a microtome. The tissues are mounted with antifade mounting medium (Invitrogen) on glass slides coated with fluorescent microspheres. Figure 7.8a shows the image of the brain tissue with a thickness of μm. The microspheres below the tissue are shown in Figure 7.8b Confocal Imaging without Wavefront Compensation The spherical aberration induced by the cover glass is initially compensated by adjustment of a..correction collar on the objective lens. The system aberration is further corrected by the DM by..measuring the wavefront aberration from a microsphere at the bottom of the cover plate using the SHWF sensor. The thickness of the brain tissue is μm. The confocal imaging system scans from the top surface to the bottom surface. The FOV is about 5 μm. The frame rate is 3 frames/second for fast scanning. To improve the SNR, 3 frames are averaged to generate the final image. Figure 7.9a shows the confocal image at the top surface, where the cell body, dendrite, and spine can be observed. Figure 7.9b shows the image at the bottom surface. Because of the aberrations induced by the tissue, it is very hard to see the dendrites and spines around the cell body Confocal Imaging with Wavefront Compensation Brain tissues with thickness of 5, 5, and μm are imaged in the AO system. A motorized Z stage under the sample focuses the HeNe laser on the microsphere at the bottom of the tissue. The wavefront 3 by Taylor & Francis Group, LLC

19 Adaptive Optical Microscopy Using Direct Wavefront Measurements 333 (a) (d) (g) (b) Pixel (c) (e) (h) Intensity Intensity Intensity With AO Without AO With AO Without AO Pixel (f) With AO Without AO Pixel (i) FIGuRE 7. (See color insert.) Confocal images with and without wavefront error correction, respectively, and the intensity profiles along the line indicated in the confocal images. (a) and (b) The images before and after correction for brain tissue with 5 μm thickness. (c) The intensity profile along the lines indicated in (a) and (b). (d) (f) The images before and after..correction and intensity profile for brain tissues with 5 μm thickness. (g) (i) The results for brain tissue with μm thickness. error induced by the sample is measured by the SHWF sensor. A stack of confocal images with a flattened mirror surface are collected by scanning along the z-axis with a range of 3 μm and step size of.5 μm between each image plane. The final image is obtained by using the maximum-intensity projection applied on these images. After turning on the wavefront correction loop, the wavefront error converges after around iterations, which takes about.35 seconds. Then the confocal images are collected with the same settings as were collected before correction. The confocal images of the brain tissue with 5 μm thickness before and after correction are shown in Figure 7.a and b, respectively (Tao et al. b). The images of the dendrite and spines are clearer after correction. The intensity profile along the line crossing the dendrite and the spine is shown in Figure 7.c. Both the signal intensity and the image contrast are improved. The signal intensity increases by 3%. The RMS wavefront error is.λ (λ = 633nm) before correction. After correction, RMS wavefront error was reduced to.λ. Figure 7.d and e show the confocal images of brain tissue with 5 μm thickness before and after correction. Because the system suffers more aberration, the image of the spines becomes dimmer. The intensity profile along the dashed line and solid line is shown in Figure 7.f. The signal intensity increases by 43%. The RMS wavefront error was reduced from.9λ to.3λ. Although the diffraction limit image is achieved, the image is still suffering from the scattering effect of the brain tissue. The increase in the signal intensity could be smaller than the theoretical calculation without consideration of the scattering effect. For the brain tissue with μm thickness, it is very hard to observe any feature as shown in Figure 7.g. After wavefront correction, the dendritic spine can be clearly observed as shown in Figure 7.h. The intensity profile is shown in Figure 7.i. The signal 3 by Taylor & Francis Group, LLC

20 334 Applications: Direct Wavefront Sensing.5.5 λ 5 (a) λ (b) (c) (d) FIGuRE 7. Wavefront measurements from a fluorescent microsphere guide-star through -μm-thick brain tissue. Wavefront error before correction (a) and after correction (b). The RMS errors for (a) and (b) are.4λ and.8λ (λ = 633 nm), respectively. Images of the microsphere guide-star before correction (c) and after correction (d). The scale bar is μm. TABle 7.3 Statistical Properties of the Strehl Ratio for Brain Tissues Strehl ratio Before correction After correction No. Thickness (μm) Mean Std Dev Mean Std Dev intensity increases by 4%. The wavefront error for the crimson guide-star before correction is shown in Figure 7.a, which suffers a large amount of spherical aberration (Tao et al. ). The RMS error is.4λ. After correction, the RMS wavefront error decreased to.8λ as shown in Figure 7.b. The images of the microsphere before and after correction are shown in Figure 7.c and d. The Strehl ratio was measured using the method described in Azucena et al. () at different positions on each sample (Table 7.3). The improvement in the Strehl ratio was approximately 4.3 for a -μm-thick sample comparison between a Commercial Confocal Microscope and the AO Confocal Microscope To compare our system s performance with a standard commercial confocal system (Leica TCS SP5 II), the resolution was investigated for a 5-μm-thick brain tissue sample on both systems using objective 3 by Taylor & Francis Group, LLC

21 Adaptive Optical Microscopy Using Direct Wavefront Measurements 335 lenses with the same NA (.) and detectors with the same-size pinholes (.9 Airy units). The transverse/ axial resolutions were improved from.3/.4 μm for the commercial system to.3/.8 μm for our AO system after correction. Although reducing the pinhole diameter can increase the resolution, the commercial system still suffers from aberration. The lateral/axial resolution for the commercial system with.5 Airy units is.9/. μm. 7.4 Using Fluorescent Proteins as Guide Stars To make a stable and fast wavefront measurement, a direct wavefront measurement method has been demonstrated, where a fluorescent microsphere injected into the sample was used as a reference source for a SHWF sensor (Azucena et al. ; Tao et al. a, b). The exposure time during wavefront sensing, typically 35 ms, is much shorter than the indirect wavefront methods (Debarre et al. 9; Ji, Milkie, & Betzig ), which reduces the possibility of phototoxicity and photobleaching. It also enables higherspeed imaging for dynamic live samples. However, this method requires the injection of fluorescent microspheres into the sample, which complicates the sample preparation procedure. The microspheres are required to cover the whole region of interest, and the distance between two microspheres should be less than the isoplanatic width (Azucena et al. ). As an invasive method, the side effects of injection to the functionality of the biological tissue need to be considered for live imaging. To overcome these disadvantages and generalize the direct wavefront sensing method, we use fluorescent proteins as laser guide-stars (Tao et al. c). Here we use fluorescent proteins that label particular cellular structures rather than specific layers such as the retina in the eye (Biss et al. 7; Diaz Santana Haro & Dainty 999). An example is green fluorescent protein (GFP), from the bioluminescent jellyfish Aequorea victoria (Lakowicz 6). The fluorophore unit is located within a barrel of β-sheet protein, which shields the chromophore from the local environment. Because of this special structure, GFP has good photostability and high quantum yields (Lakowicz, 6). This feature makes GFP a good candidate as a laser guide-star in AO microscopy. As a noninvasive fluorescent marker, GFP has been extensively used in live cell imaging. AO microscopy can be easily applied to those studies without special preparation of the samples. The possible damage to the sample from the injection of a guide-star reference bead can be avoided. Here the genetic mutant of GFP, YFP yellow fluorescent protein, was used for wavefront measurement (Patterson et al., 997) Method Figure 7. shows the system setup, which integrates an AO system into a confocal microscope. A solid-state laser (λ = 55nm) provides the excitation light for both fluorescence imaging and wavefront sensing instead of separate lasers (55 and 633 nm) for the system, shown above in Figure 7.6. The light is fed into an objective lens ( 6 water objective, NA., Olympus) and scanned on the sample in a raster pattern with two galvo scanners (65H, Cambridge Technology). The emission light from the fluorescent protein is divided by a BS with a 5/5 splitting ratio. Half of the light was collected by the PMT (H4-5, Hamamatsu), which generates the confocal image. The other half of the light is used for wavefront sensing. We are investigating the use of a flip-mirror to guide % of the fluorescent light to the SHWF sensor for wavefront sensing or to the PMT for imaging to avoid splitting the light 5/5 with the BS. Four relay lens groups make the exit pupil of the objective lens conjugate with the SHWF sensor, DM, and scanners. To minimize the amount of out-of-focus light that enters the SHWF sensor, irises I and I were placed in the light path. These irises also block stray light from the DM, scanner, and lenses. The position of the spots in the image from the wavefront sensor was detected using a crosscorrelation centroiding algorithm (Thomas et al., 6). Then an FFT reconstruction algorithm was implemented to obtain the wavefront (Poyneer, 3). To make an accurate wavefront measurement using a SHWF sensor, the diameter of the guide star should be smaller than the diffraction limit of the wavefront sensor, which is defined in Equation 7.. In our current setup, d diffraction_limit = 5.36 μm. 3 by Taylor & Francis Group, LLC

22 336 Applications: Direct Wavefront Sensing PMT SHWS Solid-state laser (55 nm) Pinhole F F3 DB BS Objectives F X Scanner I BB DM I Y Scanner Figure 7. AO confocal microscope setup for using fluorescent protein guide-stars. A solid-state laser (55 nm) is used as the excitation light source for YFP. A dichroic beam splitter (DB) separates the emission and excitation light. Light emitted from a YFP-labeled cellular structure is collected by an objective lens and split for wavefront measurement and confocal imaging by a 5/5 BS. The wavefront error is measured by a SHWS and then corrected by a DM. Defocused and stray light is blocked by irises I and I. F is an excitation filter. F3 and F are emission filters. BB is a beam blocker. A PMT located behind a pinhole collects a confocal image of the sample s fluorescence. Because the fluorescent light from a given point is proportional to the light intensity illuminating that point, the size of the guide star is determined by the illumination PSF. The PSF is calculated from the wavefront measurement using the method described in Beverage, Shack, and Descour (). For GFP at a depth of 7 μm, the diameter of the PSF with 8% of the encircled energy is.4 μm, which is small enough to be used as a guide star. To investigate the feasibility of the proposed system, a fixed brain-tissue slice from a YFP-H line transgenic mouse was prepared. Sample brain coronal sections ( μm) were cut with a microtome. The tissues were mounted on the slide with antifade reagents (Invitrogen). The spherical aberration induced by the cover plate was compensated by adjustment of a correction collar on the objective lens. The system aberration was further corrected by the DM by measuring the wavefront aberration from the top surface of the tissue. During the experiment, the confocal images were initially captured without wavefront correction. The approximate location of the GFP was identified from this initial image. Then the scanning mirror was used to steer the laser beam to the region of the GFP, and a wavefront measurement was performed. The DM corrected the aberration in a closed loop using the direct-slope algorithm (Porter et al. 6). Then the corrected confocal image of the isoplanatic region (Azucena et al. ) around the GFP guide star is captured with the optimal shape of DM as determined from the wavefront measurement. During the wavefront measurement, the laser is focused on a stationary point, which may cause photobleaching of GFP. By decreasing the laser power and increasing the exposure time of the SHWF sensor, sufficient signal can be captured by the SHWF sensor during the wavefront measurement before photobleaching. In this system, the laser power is controlled by a software and is turned down to 3 nw at the back aperture of the objective lens during wavefront sensing and turned up to μw during confocal scanning. The exposure time of the SHWF sensor could be decreased before photobleaching by increasing the laser power and using a high-speed shutter to limit the exposure time of the laser on the sample, which will be considered in the future. GFP on the dendrite and cell body of the neuron were tested as laser guide-stars at depths of 5 and 7 μm, respectively, as shown in Figure 7.3a and b. The crossed lines show the location of the laser focus. The exposure time of the wavefront measurement for the dendrite and cell body is 5 and 3 ms, respectively. Because the dendrites have less GFP than the cell bodies, longer exposure times are required to collect enough signal for accurate wavefront measurement. 3 by Taylor & Francis Group, LLC

23 Adaptive Optical Microscopy Using Direct Wavefront Measurements 337 (a) (b) Wavefront error (λ) 5 (c) 5 Wavefront error (λ) 5 (d) 5 Figure 7.3 Wavefront measurements using YFP-labeled structures as guide stars in mouse brain tissue. The excitation light source is focused on a dendrite in (a) and on a cell body of the neurons in (b). The crossed lines indicate the location of the focus point for the wavefront measurements. The wavefront measurements using a YFPlabeled structure is shown for a dendrite in (c) and a cell body in (d). The scale bar is 5 μm. The measurement errors for different numbers of photons per subaperture can be measured using the method described in Morzinski et al. (). The EM gain setting for the EMCCD in SHWF sensor was. The photons per subaperture for the wavefront measurements shown in Figure 7.3c and d are 95 and 47, which produce.3λ in measurement error. This amount of measurement error is small and improvements at this level will also depend on the errors caused by limitations of the DM and wavefront temporal variations. The RMS wavefront errors shown in Figure 7.3c and d are.74λ and.347λ (λ = 57 nm), respectively. Photobleaching is tested for the YFPs in a dendrite, because it has a lower concentration of fluorophores and thus photobleaches more quickly. Confocal images were obtained every 3 seconds during the exposure of the laser with 3 nw at the back aperture of the objective lens for wavefront.sensing. The intensity change in the focus area is shown in Figure 7.4. After the first three minutes, the intensity drops less than %. Considering the exposure time (5 ms) for the wavefront measurement, photobleaching caused by the wavefront measurement is very limited. For live samples, higher laser power can be applied because the fluorescence recovers after photobleaching. Therefore, shorter exposure times can be achieved. The line profile along two subapertures on the SHWF sensor image is shown. The confocal images for the sample are collected by scanning along the z-axis with a 3 μm range and a.5 μm step size. The final images, as shown in Figure 7.5, are achieved using the maximum intensity projection applied to the images. After turning on the wavefront correction loop, the wavefront error converges after iterations, which takes.3 seconds. The YFP on the cell body was used as a guide-star, which is located at a depth of 7 μm, as shown in Figure 7.3b. Before correction, the RMS wavefront error is.347λ. After correction, the measured wavefront error is.3λ RMS, as shown in Figure 7.5e. The confocal images before correction and after correction are shown in Figure 7.5a and b. The intensity profile along the dashed lines across a dendrite and a spine is shown in Figure 7.5f. The intensity increased by 3. The image of the dendrite and the spines are much clearer after correction with improved image contrast. We also tested the fruit-fly embryos labeled with GFP-polo and EGFP-Cnn (Tao et al., ). To test the ability of the wavefront correction at a deep depth, the confocal images with and without corrections 3 by Taylor & Francis Group, LLC

24 338 Applications: Direct Wavefront Sensing.9.8 Normalized intensity Time (minutes) FIGuRE 7.4 Photobleaching analysis. Normalized intensity at the focal point on the dendrite (a) 3 7 (b) Wavefront error (λ) 5 (c) (e) 5 Intensity 3 6 (d) With AO Without AO 4 6 μm (f) FIGuRE 7.5 Confocal fluorescence imaging of mouse-brain tissue using an YFP-labeled cell body of a neuron as a guide star. The maximum-intensity projection image within the isoplanatic region of the guide star before correction (a) and after correction (b). The dashed boxes indicate enlarged images before correction (c) and after correction (d). (e) The wavefront error after correction. (f) Intensity profiles along the dashed line in the uncorrected image (c) and along the solid line in the corrected image (d). The scale bar is 5 μm. 3 by Taylor & Francis Group, LLC

25 Adaptive Optical Microscopy Using Direct Wavefront Measurements 339 PSF PSF (a) (b) Figure 7.6 The images and PSF without (a) and with (b) correction for a cycle 4 fruit fly embryo with green fluorescent protein-polo at the depth of 83 μm. The scale bar is μm. are captured at the depth of 83 μm as shown in Figure 7.6. The GFP-polo-labeled centrosomes can be observed clearly after correction but cannot be observed before correction. The size of the PSF decreases from.7 to. μm. The Strehl ratio calculated based on the PSF shows an increase from to.7. The penetration depth for live imaging of a fruit-fly embryo is tested by performing AO correction during Z scanning from the top surface to depth of μm. The maximum-intensity projection of the scan series shows the GFP at the edge of embryo at different depths as shown in Figure 7.7a and b. Before correction, the EGFP-Cnn-labeled centrosomes can be observed only up to 6 μm depth. After correction, they can be observed below a depth of 8 μm. Using the 3D view function in ImageJ with the resampling factor of two, the 3D images of the fruit-fly embryo show that the penetration depth increases from 6 to 95 μm, with more than a 5% increase in imaging depth as shown in Figure 7.7c and d. Without correction, the RMS wavefront error reaches to.8λ when the imaging depth goes to 9 μm. The decrease in the Strehl ratio shows the degradation of the optical performance with the imaging depth as shown in Figure 7.7e. After correction, even at the depth of 9 μm, the system can still achieve a Strehl ratio of.6 with an RMS wavefront error of.λ. Aside from improving the penetration depth, the system also improves the optical resolution. Although the EGFP-Cnn-labeled centrosomes can be observed at a depth of 6 μm without AO, the resolution is still poor because of the aberrations. Before correction, the size of the PSF is.67 μm at a depth of 6 μm. After correction, it decreases to. μm as shown in Figure 7.7f. At a depth of 9 μm, it shows a significant improvement of the PSF by a factor of nine. 7.5 Discussion and Conclusion One of the challenges in designing an SHWF sensor is imposed by the amount of light the reference source can provide. Polystyrene microspheres are loaded with fluorescent dye, and the light emitted is proportional to the radius cubed; thus, smaller beads provide less light. The size of the beads should be smaller than the diffraction limit of one subaperture of the Hartmann wavefront sensor. Note that this is larger than the diffraction limit of the microscope aperture by the ratio D (size of the aperture)/d LA, as shown in Equation 7.. Since the diffraction limit of the microscope is inversely proportional to the NA, smaller beads are needed for higher-na systems. Fortunately the light gathered by the objective also increases with increasing NA (light-gathering power ~ NA ). Increasing the wavefront sampling by a factor of four increases the size of the microsphere radius by a factor of two and the amount of light emitted by a factor of eight. Current results show that for a 4 objective with an NA of.75, a μm fluorescent microsphere provides enough light to run the AO system loop with a ms period. If the size of the bead was reduced by a factor of to nm in radius, we could still obtain a good correction by using the AO system but with the disadvantage of a lower SNR. This could be compensated by increasing the AO loop period to ms or by reducing the number of pixels used for each subaperture. Both these approaches come from the fact that the SNR of the SHWF sensor can be improved by increasing the integration time of the CCD camera or by using fewer pixels to detect the movement of the centroids. 3 by Taylor & Francis Group, LLC

26 34 Applications: Direct Wavefront Sensing (a) (b) 8 μm 4 μm 6 μm (c) (d) 6 μm 95 μm.8.5 Without AO With AO Strehl ratio.6.4. Without AO With AO PSF size (μm) Depth (μm) (e) Depth (μm) (f) 8 FIGuRE 7.7 (See color insert.) Comparison of penetration depths between without and with correction for imaging of cycle 3 fly embryos with EGFP-Cnn label. (a) (b) The maximum intensity projection of the scan series from the top surface to μm with and without adaptive optics. (c) (d) The three-dimensional reconstructions with and without AO. (e) (f) The Strehl ratio and PSF size change for different depth. The black and gray lines indicate without and with AO, respectively. The scale bar is μm. 3 by Taylor & Francis Group, LLC /5/ :53:7 PM

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